Square of a number ending with a 5

It is very simple to calculate the square of a decimal number ending with a 5 without a calculator, or even pencil and paper:

• Chop off the 5;
• Multiply the rest (x) by itself plus 1 (x*(x+1));
• Append 25.

That's all it takes.

For example, the square of 25 is:

• Chop off 5, you get 2;
• Multiply 2 by 2 + 1, i.e., 2 * 3 = 6;
• Append 25, hence 25*25 = 625.

Another example, the square of 205 is:

• Chop off the 5, you get 20;
• Multiply that by 20 + 1 = 21, i.e., 20 * 21 = 420;
• Append 25, hence 205*205 = 42025.

For anyone who enjoys knowing why this sort of thing works:

x² =
x² -5x+5x -5²+5² =
x(x-5)+5(x-5)+5² =
(x-5)(x+5)+5² =
(x-5)(x+5)+25

...which is true for any value of x, but is easiest to calculate in your head when x-5 and x+5 are multiples of ten.